DOE stands for Design of Experiments. You vary several inputs in a planned pattern to investigate their effects and interactions. This guide walks through a full two-level factorial experiment.
1. Define a specific question
Start with a decision: Which settings improve bond strength without exceeding the allowable processing time? “Understand the process” is too broad on its own.
Describe the process, material, baseline and intended scope. Decide in advance what improvement would matter in practice. This helps prevent selecting only striking results after seeing the data.
Your next step: Record the question, response, unit and relevant improvement in your project.
2. Check the measurement
The response is the outcome measured for each run. Use a consistent method, unit and measurement time. Your measurement system must reliably distinguish changes of interest.
Check resolution, repeatability, operator influence and calibration where appropriate. Destructive testing needs comparable specimens. A better design cannot compensate for an unreliable measurement system.
Your next step: Write a short measurement procedure and check measurement variation before the main experiment.
3. Choose factors and levels
Factors are inputs you deliberately change, such as temperature, pressure or material type. Identify plausible causes with the people who work with the process.
A two-level design uses two distinct settings per factor. For numbers these are usually a low and high setting; categories could be two materials. Every combination must be feasible and safe. Individually acceptable settings do not guarantee an acceptable combination.
Your next step: Check every combination for feasibility. Include units in factor names.
Try it in the free app →4. Select an appropriate design
A full two-level factorial tests every combination: 4 for two factors, 8 for three, 16 for four and 32 for five. Each complete replicate multiplies that number. This free app supports two to five factors and one to five independent runs per combination.
Fractional factorial designs reduce runs but can alias effects. Screening can help with many factors. Curvature and an interior optimum require additional levels or suitable response surface designs. Mixture experiments need dedicated models because the proportions sum to a fixed total.
Your next step: Use this app for full two-level factorial designs. Choose a suitable method first for other questions.
Try it in the free app →5. Plan replication and resources
An independent replicate means preparing the experimental unit and conditions again and repeating the run. Measuring the same part three times describes measurement variation; it does not replace three independent process runs.
Two runs per combination allow within-combination variation to be estimated. Adequacy depends on variation, the smallest effect of interest and the required evidence. The app does not calculate power or guarantee detection with a particular number of runs.
Your next step: Budget material, setup time and independent replicates. Use pilot data to refine sample size planning.
6. Consider order and nuisance variables
Random order helps avoid systematically mixing time trends with factor effects. Still record date, material batch, operator and unusual events. Process warm-up can affect results even with randomization.
Different experimental days may call for blocking. Hard-to-change settings, such as a large furnace temperature, may require a split-plot design. This app assumes fully randomizable runs and does not model blocks or split-plot structures.
Your next step: Generate the randomized order before the first run and retain it throughout execution.
7. Run and document the experiment
Follow the planned sequence. Keep constant conditions, waiting times and measurement methods consistent. Record actual settings and deviations rather than just copying target settings.
A missing value is not zero. Document decisions to repeat failed runs and do not remove inconvenient results without a technical reason. The app requires a complete plan for analysis so missing values cannot distort balanced effect calculations.
Your next step: Enter one response per run. Use project notes for deviations and observations.
8. Understand effects and interactions
A main effect here is the mean at the high level minus the mean at the low level, averaged across other factors. An effect of +8 MPa therefore means an average increase of 8 MPa over the tested range.
An interaction means that the effect of one factor depends on another factor’s setting. Different slopes in the interaction plot reveal this dependency. The app shows main effects and two-factor interactions, not higher-order interactions. Bars represent effect size, not a significance test.
Your next step: Read interactions alongside main effects. Consider both magnitude and practical relevance.
Try it in the free app →9. Make a supported decision
The best observed combination has the most favorable mean among the tested settings. It is not a proven global optimum or automatically a technically or economically suitable choice.
With independent replicates the app shows pooled within-combination standard deviation and the standard error of an effect. These require independent errors and comparable variance. Inspect observations and unusual events as well. The app does not provide p-values, confidence intervals, residual diagnostics or formal model validation.
Your next step: Weigh benefits against cost, process limits and uncertainty. Document your decision.
10. Confirm the improvement
Check the selected settings with new independent runs. Where possible compare against the baseline under comparable conditions. Define success criteria before collecting confirmation data.
After confirmation, introduce the setting into operations in a controlled way. Update work instructions and monitor whether the benefit persists across batches, operators and time. One favorable result is insufficient.
Your next step: Record the confirmation plan, owners and results, including the scope and remaining evidence gaps.
Example: improve bond strength
Synthetic teaching example: temperature 160/180 °C, pressure 3/5 bar and time 20/30 s. The aim is greater strength in MPa. These are not recommended process settings. Eight combinations are independently executed twice, giving 16 runs.
| Temperature °C | Pressure bar | Time s | Responses MPa |
|---|---|---|---|
| 160 | 3 | 20 | 45.5 / 46.5 |
| 180 | 3 | 20 | 47.5 / 48.5 |
| 160 | 5 | 20 | 43.5 / 44.5 |
| 180 | 5 | 20 | 57.5 / 58.5 |
| 160 | 3 | 30 | 47.5 / 48.5 |
| 180 | 3 | 30 | 49.5 / 50.5 |
| 160 | 5 | 30 | 45.5 / 46.5 |
| 180 | 5 | 30 | 59.5 / 60.5 |
Temperature calculation: mean at 180 °C = 54 MPa; at 160 °C = 46 MPa. The main effect is 54 − 46 = +8 MPa. Pressure has an effect of +4 MPa and time +2 MPa. The temperature-pressure interaction is +6 MPa using ±1 coding.
At low temperature, higher pressure changes the mean by −2 MPa; at high temperature, by +10 MPa. This illustrates why pressure should not be interpreted alone. The best observed combination is 180 °C, 5 bar, 30 s with a mean of 60 MPa.
The grand mean is 50 MPa. The pooled standard deviation is about 0.7071 MPa with 8 degrees of freedom; the standard error of an effect is about 0.3536 MPa. An operational decision would require new confirmation runs and a review of process limits.
Open the app and choose “Load example” →Method and sources
The app calculates balanced contrasts in full two-level factorial designs. Main and pair interaction effects are 2/N × Σ(sᵢ × yᵢ), where sᵢ is the factor code or product of codes. Error variance is estimated only from replicates within identical combinations; an effect’s standard error is 2s/√N.
NIST/SEMATECH: Process Improvement · Modeling DOE data · Confirmatory runs